Elastic rod Rigid bar q = 5 kN/m 0.75 m |P = 10 kN A B -2.5 m- -0.75 m- PROBLEM 2.2-2

The figure below shows a section of a column subjected to load P, which is applied 50 mm from the midline of the section's web. The column is made from material, which has an allowable normal stress of 180 MPa (both in tension and compression). The area of the section is 10050 mm?; the principal moments of inertia Imar = 146.554x106 mm and Imin 20.076x10° mm*. !! Determine the maximum allowable load P. 15 mm 150 mm 15 mm 150 mm 50 mm 15 mm 100 mm 100 mm 1194.6 kN 363.6 kN 1809.0 kN O 516.4 kN O 189.5 kN

A vertical load P is applied at the center B of the upper section of a homogeneous frustum of a circular cone of length L, minimum radius rB, and maximum radius rA, as shown in the figure below. It is made of a material with a modulus of elasticity E. Neglect the effect of its weight. Use the following values: rA = 2 in, rB = 0.5 in, L = 3 ft, E = 30 (103 ) ksi, and P = 1800 lbf. Discretize the original geometry into three equal-length finite elements and (a) Compute all the nodal displacements. (b) Compute all the element axial stresses. (c) Plot the displacement field from the finite element method solution. (d) Plot the axial stress field from the finite element method solution.

A steel bar with a circular cross section, AC, is built in at both ends (A and C) and is subjected to a 300N point load at B, 300mm from point A, as shown in the figure below. The bar has a diameter of 8 mm and the material has a Young's modulus of 200GPa. Determine the magnitude of the reaction force at A? O O O O 380 N 150 N Don't Know 210 N 300 N 300mm B 300 N 700mm